Problem solving is an art that is central to understanding and ability in mathematics. With this series of books the authors have provided a selection of problems with complete solutions and test papers designed to be used with or instead of standard textbooks on algebra. For the convenience of the reader, a key explaining how the present books may be used in conjunction with some of the major textbooks is included. Each book of problems is divided into chapters that begin with some notes on notation and prerequisites. The majority of the material is aimed at the student of average ability but there are some more challenging problems. By working through the books, the student will gain a deeper understanding of the fundamental concepts involved, and practice in the formulation, and so solution, of other algebraic problems. Later books in the series cover material at a more advanced level than the earlier titles, although each is, within its own limits, self-contained.

Preface; Background reference material; 1. Matrices and linear equations; 2. Inverses and determinants; 3. Eigenvalues and diagonalisation; 4. Vector spaces; 5. Linear mappings; 6. Inner product spaces; Solutions to chapter 1; Solutions to chapter 2; Solutions to chapter 3; Solutions to chapter 4; Solutions to chapter 5; Solutions to chapter 6; Test paper 1; Test paper 2; Test paper 3; Test paper 4.